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Suggestions for teaching Mathematical Statistics

  • 1.  Suggestions for teaching Mathematical Statistics

    Posted 08-18-2016 16:03

    Dear All,

    I have been teaching a Masters level course in Mathematical Statistics for several years out of Casella and Berger's textbook. The syllabus includes optimal estimators (Cramer-Rao, Rao-Blackwell, Lehmann-Scheffe), hypothesis testing, confidence intervals, convergence. However, it seems to me that the material is a bit outdated in the age of big data, sparse estimation, and multiple testing - especially at the Masters level. Therefore I was considering updating the course content.

    I would like to know if anybody out there feel the same and if you have any suggestions for possible topics to include and to drop. Suggestions on textbooks on a modern version of Mathematical Statistics are very welcome too.

    Thank you all in advance for the feedback!

    Best,

    Giovanni Petris

    ------------------------------
    Giovanni Petris, PhD
    Professor
    Director of Statistics
    Department of Mathematical Sciences
    University of Arkansas - Fayetteville, AR 72701
    ------------------------------


  • 2.  RE: Suggestions for teaching Mathematical Statistics

    Posted 08-19-2016 03:21

    Dear Giovanni, please have a look at https://www4.ceda.polimi.it/manifesti/manifesti/controller/ManifestoPublic.do?EVN_DETTAGLIO_RIGA_MANIFESTO=EVENTO&c_insegn=095967&aa=2014&k_cf=225&k_corso_la=487&ac_ins=0&k_indir=MST&lang=EN&tipoCorso=ALL_TIPO_CORSO&semestre=2&codDescr=095967&idItemOfferta=112780&idRiga=178420&jaf_currentWFID=main

    Here you can find the following program: Exploring a multivariate dataset: descriptive statistics and graphical displays. The geometry of a multivariate sample. The distance induced by the covariance matrix. Analysis of covariance structure: principal components and dimensional reduction. Inferences about a mean vector: Hotelling T^2 test. Confidence regions and simultaneous comparisons of component means. Multiple comparisons methods. ANOVA and MANOVA. Discrimination, classification, clustering: Statistical classification: model, miscalassification costs and prior probability. Bayesian supervised classification and the Fisher approach to discriminant analysis. Alternative approaches to classification: logistic regression, CART. Similarity measures. Unsupervised classification; hierarchical and nonhierarchical methods. Multidimensional scaling. Functional data Analysis: smoothing and representing functional data. Dimensional reduction: functional principal components. Allignment of functional data: amplitude and phase variability. Registration procedures. Classiffication with functional data. Mixed effects models: introduction to linear and generalized multilevel models. Multivariate logistic regression models for binary data: classification and prediction. Multilevel models for longitudinal data. Growth curves with autocorrelated residuals. Models for multivariate repente measures. Introduction to statistical models for the analysis of spatial data.

    given to students of Master in Mathemathical Engineering by Piercesare Secchi, a colleague, director of Department of Mathematics, Politecnico of Milan. This could be a starting suggestion.

    ------------------------------
    Elio Piazza
    retired (but still teaching) former professor of Statistics
    Politecnico of Milan

    Original Message


  • 3.  RE: Suggestions for teaching Mathematical Statistics

    Posted 08-19-2016 05:32
    Dear Giovanni,
    I think it's a really good idea.  However, you might want to consider some
    practical issues in implementing it, outside of planning the content.

    It is a good idea to get your colleagues' feedback about such a redesign.
    Changing an existing graduate course may also require graduate school approval,
    even if your department favors the idea.  There are two things I suggest
    as possible intermediate steps before a full-fledged redesign of an existing course.

    1.  You might consider teaching a `topics'/seminar course first
     to get a feel for what new topics can be covered in a semester.
     It is easier to get approval for a topics course.  In fact, it may just require 
     talking to your chair and/or graduate coordinator and putting it in the bulletin.
     Once you have successfully taught `new' material in another course, 
     it may be easier to get approval for including it in a redesigned course.

    2. Another possible intermediate step is to introduce a regular MS or PhD class,
     (i.e. not a seminar/topics class) with some of the more `modern' areas that you mention.
     This could also be done after offering the topics class but before redesigning your core
     graduate math stat class.  Alternatively, depending on your colleagues support for it,
     you could bypass the topics class, and offer a regular class, with a title like
     "Modern Statistical theory and methods."

    Good luck!  I would enjoy hearing how it goes.

    Best,
    Sudip
    ---------------------
    Sudip Bose,
    Department of Statistics,
    The George Washington University



    Original Message


  • 4.  RE: Suggestions for teaching Mathematical Statistics

    Posted 08-19-2016 11:01

    Dear Giovanni,

    I would take a look at: 

    Computer Age Statistical Inference: Algorithms, Evidence, and Data Science (Institute of Mathematical Statistics Monographs), Sep 30, 2016, by Bradley Efron and Trevor Hastie. You can see the Table of Contents on Amazon

     

    ------------------------------
    William Fairley
    Senior Statistician and President
    Analysis & Inference, Inc.

    Original Message


  • 5.  RE: Suggestions for teaching Mathematical Statistics

    Posted 08-19-2016 11:56

    I'd go with Gelman's Bayesian Data Analysis and teach the Stan language.

     

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    Original Message


  • 6.  RE: Suggestions for teaching Mathematical Statistics

    Posted 08-19-2016 13:47

    Any course in Big Data should contain some practical approaches. Having worked with large data sources for 20+ years the biggest lesson is to understand that when you have a LOT of data that many results will be significant. Whether it is simple T-Tests, confidence intervals, or complex multivariate models.

    The key, as an analyst is to know how to sort out the wheat from the chaff. This takes Subject Matter Expertise (SME) and a good dose of common sense. It is also helpful to have a lot of general knowledge. An analyst should always get SME either through personal education or have a consultant with that knowledge. There is nothing more embarrassing that presenting a result to a client or audience only to have it pointed out that the result makes no sense whatsoever. And this can happen with Big Data more often than not.

    ------------------------------
    Michael Mout
    MIKS

    Original Message


  • 7.  RE: Suggestions for teaching Mathematical Statistics

    Posted 08-22-2016 08:05

    You might look at Larry Wasserman's All of Statistics,

    which has material for the usual topics but also

    background for machine learning and big data topics.

    See All of Statistics - A Concise Course in Statistical Inference | Larry Wasserman | Springer

    For more on theory relevant to machine learning 

    see his All of Nonparametric Statistics.

    Also his videos on stat theory for machine learning are online.

    ------------------------------
    David Rindskopf
    CUNY Graduate Center

    Original Message


  • 8.  RE: Suggestions for teaching Mathematical Statistics

    Posted 08-22-2016 08:16

    Dear Giovanni:

    I have a draft version of a mathematical statistics textbook.  I am looking for someone who would be willing to class-test the textbook.

    Larry Leemis

    Department of Mathematics

    leemis@math.wm.edu

    757-221-2034

    ------------------------------
    Lawrence Leemis
    College of William & Mary

    Original Message


  • 9.  RE: Suggestions for teaching Mathematical Statistics

    Posted 08-23-2016 03:35
    Edited by Christian Graf 08-23-2016 03:36

    Dear Giovanni,

    I am teaching on Big Data in an industrial environment. From my point of view, the basic statistical concepts apply and you should continue to teach those to form the mindset a data analyst requires.

    However, when it comes to big data, automated analysis of data quality and reproducibility of results becomes ever more important. I'd suggest to include this topic explicitely in your lecture.

    For a start I recommend the following articles:

    Puts et al.: Finding errors in Big Data: Finding errors in Big Data - Puts - 2015 - Significance - Wiley Online Library

    Wiley remove preview
    Finding errors in Big Data - Puts - 2015 - Significance - Wiley Online Library
    Beate Franke, Jean-François Plante, Ribana Roscher, En-shiun Annie Lee, Cathal Smyth, Armin Hatefi, Fuqi Chen, Einat Gil, Alexander Schwing, Alessandro Selvitella, Michael M. Hoffman, Roger Grosse, Dieter Hendricks, Nancy Reid, Statistical Inference, Learning and Models in Big Data, International Statistical Review, 2016 Wiley Online Library
    View this on Wiley >

    Wickham, Hadley: Tidy Data. Journal of Statistical Software - see http://www.jstatsoft.org/

    Also Roger D. Peng (Biostatistics) has published on this topic.

    Best regards,
    Christian

    ------------------------------
    Christian Graf
    Dipl.-Math.
    Qualitaetssicherung & Statistik

    "To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of."

    Ronald Fisher in 'Presidential Address by Professor R. A. Fisher, Sc.D., F.R.S. Sankhyā: The Indian Journal of Statistics (1933-1960), Vol. 4, No. 1 (1938), pp. 14-17'

    Original Message